Problem 5
Question
Find the sums. $$ -14+(-20) $$
Step-by-Step Solution
Verified Answer
The sum is -34.
1Step 1: Understanding the Problem
We need to find the sum of -14 and -20. This involves adding two negative numbers. When we add negative numbers, the result is also negative and can be found by adding the absolute values and then putting a negative sign in front.
2Step 2: Calculate the Absolute Values
Calculate the absolute values of the numbers involved. The absolute value of -14 is 14, and the absolute value of -20 is 20.
3Step 3: Add the Absolute Values
Add the absolute values we found: \( 14 + 20 = 34 \).
4Step 4: Assign a Negative Sign
Since both numbers are negative, their sum will also be negative. Therefore, the sum of -14 and -20 is -34.
Key Concepts
Addition of IntegersAbsolute ValueSum of Negative Numbers
Addition of Integers
When it comes to the addition of integers, it’s important to remember that integers include all whole numbers, both positive and negative, as well as zero.
Understanding how to add integers is a foundational skill in math. It can seem tricky at first, especially when negative numbers are involved, but it gets easier with practice. Here's a simple way to think about it:
When adding integers, consider a number line. Moving to the right indicates positive numbers, while moving to the left involves negative numbers. Knowing how to visualize these steps helps in mastering the concept of adding integers.
- Same sign: If both integers have the same sign (both positive or both negative), you add their absolute values and keep the common sign.
- Different signs: If they have different signs, you subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value.
When adding integers, consider a number line. Moving to the right indicates positive numbers, while moving to the left involves negative numbers. Knowing how to visualize these steps helps in mastering the concept of adding integers.
Absolute Value
The concept of absolute value is crucial when working with integers, especially negative ones. Absolute value refers to the distance of a number from zero on the number line, regardless of direction. Therefore, the absolute value is always a non-negative number.
For example:
Here's a helpful tip: think of absolute values like measuring distances. Just as distances are always positive, absolute values reflect magnitudes without considering direction (or sign). This is why when we add negative numbers, we often focus on their absolute values first. It's like adding two distances together, then attributing a negative sign if needed, based on the original numbers.
- The absolute value of -14 is 14.
- The absolute value of -20 is 20.
Here's a helpful tip: think of absolute values like measuring distances. Just as distances are always positive, absolute values reflect magnitudes without considering direction (or sign). This is why when we add negative numbers, we often focus on their absolute values first. It's like adding two distances together, then attributing a negative sign if needed, based on the original numbers.
Sum of Negative Numbers
Finding the sum of negative numbers might seem daunting, but it follows a straightforward process.
When you add two negative numbers, you essentially combine their absolute values, since both numbers "pull" the final sum into the negative region.
Let's break it down further:
- First, find the absolute values. For example, with -14 and -20, you get 14 and 20.
- Next, add these absolute values: 14 + 20 = 34.
- Finally, because you started with two negative numbers, place a negative sign in front of the result: -34.